Test: The Concept of Potential Energy (June 23) - JEE MCQ

We know that the total work done by gravity is always equal to the gravitational force in magnitude as it is a conservative force and as because no other non conservative force acts upon the body we can say the mechanical energy remains conserved. Thus we get the potential energy at top is exactly equal to KE just before the ball hitting the ground.

Change in GPE (Gravitational Potential energy) = mass x gravity x change in height
500 = 10 x 10 x change in height 

500 / 100 = change in height 

So, height from where it begins its dive = 5 m

mass = 50 x 100 = 5000 kg, g = 10 m/s²,  h = 10 m
Potential energy gained = mgh = 5000 x 10 x 10 = 5 x 10⁵ J

In A stretched bow. Compressed gas, compressed or elongated spring there is elastic potential energy but the lifted weight there is gravitational force, so the odd one here is lifted weight.

As the final velocity after the action of all forces is 0, therefore the person has 0 net acceleration.

And, as we know that

F_net = m.a_net

_{Therefore, the net force is 0 and hence, the net work done is also 0.}

The graphs are parabolas as the potential and kinetic energy vary as x².

 

The law of conservation of energy states that: the total mechanical energy of a system remains unchanged (constant) in any isolated system of objects that interact only through conservative forces. In other words, it states that: the energy may neither be created nor destroyed, but transferred from a form of energy to another. The total mechanical energy, E, is defined as:[ E = K + U] Where K is the total kinetic energy and U is the total potential energy of the system.
 
The conservation law of energy is , therefore, [E_i = E_f ],Where Ei and Ef are the initial and final energies, respectively. That implies to K_i + U_i = K_f + U_f

Potential Energy is any type of stored energy. It can be chemical, nuclear, gravitational, or mechanical. Kinetic Energy is found in movement. Nuclear power plants change the nuclear potential energy of uranium or plutonium into electricity too.

For a variable force, the work done can be expressed as a definite integral of force over displacement for any system.In case of a variable force, the is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as Fs = -kx, where k is the spring constant and x is the displacement of the object attached. We can see that this force is proportional to the displacement of the object from the equilibrium position, hence the force acting at each instant during the compression and extension of the spring will be different. Thus, the infinitesimally small contributions of work done during each instant are to be counted in order to calculate the total work done.